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Pré-Publication, Document De Travail Année : 2022

SINGULAR MODULES FOR AFFINE LIE ALGEBRAS, AND APPLICATIONS TO IRREGULAR WZNW CONFORMAL BLOCKS

Résumé

We give a mathematical definition of irregular conformal blocks in the genus-zero WZNW model for any simple Lie algebra, using coinvariants of modules for affine Lie algebras whose parameters match up with those of moduli spaces of irregular meromorphic connections: the open de Rham spaces. The Segal-Sugawara representation of the Virasoro algebra is used to show that the spaces of irregular conformal blocks assemble into a flat vector bundle over the space of isomonodromy times à la Klarès, and we provide a universal version of the resulting flat connection generalising the irregular KZ connection of Reshetikhin and the dynamical KZ connection of Felder-Markov-Tarasov-Varchenko.
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Dates et versions

hal-03748599 , version 1 (09-08-2022)
hal-03748599 , version 2 (12-06-2024)

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  • HAL Id : hal-03748599 , version 1

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Giovanni Felder, Gabriele Rembado. SINGULAR MODULES FOR AFFINE LIE ALGEBRAS, AND APPLICATIONS TO IRREGULAR WZNW CONFORMAL BLOCKS. 2022. ⟨hal-03748599v1⟩
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